The 3GPP LTE-A based cellular network [1] together with the IEEE 802.16m based cellular network are the only two cellular networks classified as 4G cellular networks by the international telecommunications union. Some key attributes that a 4G uplink must possess are the ability to support a peak spectral efficiency of 15 bps/Hz and a cell average spectral efficiency of 2 bps/Hz, ultra-low latency and bandwidths of up to 100 MHz. To achieve these ambitious specifications, the 3GPP LTE-A uplink is based on a modified form of the orthogonal frequency-division multiplexing based multiple-access (OFDMA) [1]. In addition, it allows precoded multi-stream (precoded MIMO) transmission from each scheduled user as well as flexible multi-user scheduling. Notice that while OFDMA itself allows for significant spectral efficiency gains via channel dependent frequency domain scheduling, multi-user multi-stream communication promises substantially higher degrees of freedom [2]. Our focus in this paper is on the 3GPP LTE-A uplink (UL) and in particular on MU MIMO scheduling for the LTE-A UL. Predominantly, almost all of the 4G cellular systems that will be deployed will be based on the 3GPP LTE-A standard [1]. This standard is an enhancement of the basic LTE standard which is referred to in the industry as Release 8 and indeed deployments conforming to Release 8 are already underway. The scheduling in the LTE-A UL is done in the frequency domain where in each scheduling interval the scheduler assigns one or more resource blocks (RBs) to each scheduled user. Each RB contains a pre-defined set of consecutive subcarriers and consecutive OFDM symbols and is the minimum allocation unit.
The goal of this work is to design practical uplink MU-MIMO resource allocation algorithms for the LTE-A cellular network, where the term resource refers to RBs as well as precoding matrices. In particular, we consider the design of resource allocation algorithms via weighted sum rate utility maximization that account for finite user queues (buffers) and finite precoding codebooks. In addition, the designed algorithms comply with all the main practical constraints on the assignment of RBs and precoders to the scheduled users. Our main contributions are as follows:
1) We first assume that users can employ ideal Gaussian codes and that the base-station (BS) can employ an optimal receiver. We then enforce user rates to lie in a fundamental achievable rate region of the multiple access channel which is a polymatroid and show that the resulting resource allocation problem is NP-hard. We prove that the resource allocation problem can however be formulated as the maximization of a monotonic sub-modular set function subject to one matroid and multiple knapsack constraints, and can be solved using a recently discovered polynomial time randomized constant-factor approximation algorithm [3]. We also adapt a simpler deterministic greedy algorithm and show that it yields a constant-factor approximation for scenarios of interest.
2) We then consider scenarios where users employ codes constructed over finite alphabets. In this case the mutual information terms needed to specify an achievable rate region do not have closed form expressions. On the other hand the achievable rate region obtained for Gaussian alphabets can be a loose outer bound. Consequently, we obtain a tighter outer bound which is also a polymatroid. As a result all algorithms developed for Gaussian alphabets can be reused after simple modifications. Finally, we demonstrate the superior performance of our proposed algorithms via simulations using a realistic channel model.